Sadio Mane scored a 93rd-minute winner at Loftus Road to put Southampton two points clear of fourth-placed Manchester United, who play on Sunday, and only four behind Manchester City.
“I still look down more than up,” Koeman said.
“Maybe in three weeks it will be different, but we are watching the teams around us at the moment and behind us. That’s our focus, rather than second or first place.
“It’s not all about the top four places in the table.
“We are trying to reach a European position for next season, that is the target.
“Seventh place may be enough for that or sixth.”
Southampton looked on course for a third consecutive game without a win, after defeats to Crystal Palace in the FA Cup and Swansea in the league.
Mane’s injury-time strike, however, continued the team’s charge for the Champions League spots ahead of crucial matches at home to West Ham United and Liverpool.
“How we played today and the result was very important,” Koeman added.
“In a season you always have some key moments and one of these was today.
“After last week’s defeat, we needed to show how we like to play football and to have a good result and get three points.
“That’s very good. It’s our fourth win away in a row and that’s fantastic.”
The only negative for Southampton saw defender Matt Targett taken to hospital following a head collision in the first half.
“The doctors say he is under control,” Koeman said.
“That is very good news because when something like that happens on the pitch, it can be difficult and dangerous.”